Please note special location. This is a report on joint work in progress with T. Kragh, wherein we prove that a closed exact Lagrangian in a cotangent bundle is simply homotopy equivalent to the base. I will explain the two main ingredients of the proof: (i) realising the Whitehead torsion of the projection to the base as the torsion of a Floer theoretic map and (ii) using a large Hamiltonian deformation to deform the Floer complexes in such a way that this torsion can be shown to be trivial by an action filtration argument.